Point M is the midpoint of line JK. If JM is 6x-7 and MK is 2x+3 what is JK?
JK = 6x-7 + 2x+3 = 8x - 4
6x-7 = 2x +3
Solve for x and put value in first equation.
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6x-7=2x+3
-2x -2x substitute x
4x-7=3 6(5/2)-7
+7 +7 15-7=8
4x=10 Number 8 is the answer.
divide both by 4. Then you will get x=5/2. ^^^
To find the length of line JK, we need to understand that a midpoint divides a line segment into two equal parts. Therefore, if point M is the midpoint of line JK, we can set up an equation using the given information.
Let's start by equating the lengths of the two smaller line segments to find the value of x since JM and MK are represented with variables.
Given: JM = 6x - 7 and MK = 2x + 3
Since M is the midpoint, JM = MK
So, we can set up the equation: 6x - 7 = 2x + 3
To solve for x, we need to isolate the variable on one side of the equation. Let's subtract 2x from both sides and add 7 to both sides:
6x - 2x - 7 = 2x - 2x + 3 + 7
4x - 7 = 10
Next, let's add 7 to both sides:
4x - 7 + 7 = 10 + 7
4x = 17
To solve for x, divide both sides by 4:
(4x) / 4 = 17 / 4
x = 17 / 4
Now that we have found the value of x, we can substitute it back into either JM or MK to find the respective lengths. Let's use JM = 6x - 7:
JM = 6(17 / 4) - 7
JM = 102 / 4 - 7
JM = 25.5 - 7
JM = 18.5
Similarly, the length of MK can be found by substituting the value of x into MK = 2x + 3:
MK = 2(17 / 4) + 3
MK = 34 / 4 + 3
MK = 8.5 + 3
MK = 11.5
Finally, to find the length of line JK, we add the lengths of JM and MK:
JK = JM + MK
JK = 18.5 + 11.5
JK = 30
Therefore, the length of line JK is 30 units.